Abstract: In this talk we do introduce surrogate approaches by combining model reduction with physics informed machine learning for applications in design, optimisation, as well as digital twins. Reduced-order models (ROMs) are essential for enabling efficient and accurate simulations of complex physical phenomena, particularly in Computational Fluid Dynamics (CFD) and fluid-structure interaction. We do focus on recent advancements in enhancing ROM techniques to address the challenges of real-time, multi-query, and multi-physics applications. We will explore strategies to improve the accuracy and efficiency of ROMs by integrating advanced methodologies such as neural operators and optimisation-based frameworks. These approaches leverage both physics-based insights and data-driven models to create enhanced ROMs that outperform traditional methods in terms of generalisation and computational cost. Applications to CFD, including turbulent and compressible flows, demonstrate the impact of these improvements in achieving precise and reliable solutions. These strategies extend the applicability of ROMs to complex multi-physics and multi-scale problems, offering new possibilities for simulation-driven discovery and design. This talk underlines their transformative potential in advancing computational science and engineering by highlighting cutting-edge techniques for enhancing ROMs.